Investigations Blog

Robot Fingers and Multiplicative Structure

In a blog post over a year ago, I wrote about the importance of using story contexts to support students in developing mental images of the operations. In that post, I concluded: “Along with pictures, drawings, diagrams, equations, and physical models, story contexts are critical parts of a student’s repertoire of representations.  In fact, it is often the case that three kinds of representations are in play: a numerical representation, a picture or diagram, and a story.  Moving among these to...

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“Is 100 a Teen Number?” Part 2

What follows is a lightly edited version of the second part of an end-of-Kindergarten discussion about the teen numbers. In Part 1, students took up the question of whether 100 is a teen number. That conversation built on a previous one, about why there are so many 1s in the teen numbers. At a certain point in the conversation about whether 100 is a teen number, the discussion began circling around the same ideas, ones that had already been shared. At that point, the teacher made a decision to...

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“Is 100 a Teen Number?” Part 1

Not long after I witnessed a Kindergarten conversation about why there are so many 1s in the teen numbers, I visited the same classroom. This time, it was Nicole who asked a question that knocked my socks off. “I wonder if 100 is a teen number?” When I asked why she thought it might be she said, “Because it starts with a 1.” Her partner nodded, nudged her to take her turn, and they returned to their game. Several days later, I returned, for their end-of-unit discussion about the teen numbers....

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Who Gets Challenged to Extend Their Thinking? A Conversation About Differentiation

In conversations about differentiation, strategies to scaffold learning for students who need more support, and strategies to extend the learning for students who are ready for more challenge often come up. One topic that is rarely considered however, is the importance of finding ways to offer students who typically need more support, opportunities to think about a task in ways that will extend their thinking about the mathematics. In the following conversation, excerpted from the Supporting...

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Are There Going to Be More Than 20? More Than 50?

Many of us were taught to “estimate” in elementary school. Maybe we were asked how many jellybeans there were in a jar. Or asked to round before finding the answer to a computation problem. But for many of us there was little connection between those activities and actually solving problems. I would argue that estimating — determining what an approximate and reasonable answer might be — should be a part of the process of solving problems. A visit I made to a 1st grade classroom at the end of...

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“Why are there so much 1s in these numbers?”

Last spring, I visited a Kindergarten classroom near the end of the year. Students were participating in a Math Workshop focused on the teen numbers, choosing among activities that asked them to identify and recognize teen numbers; to represent them in several different ways (e.g. on Ten Frames, with cubes, with numerals); and, ultimately, to come to see them as being composed of ten ones and some numbers of ones.  I wandered over to Stella, who was playing Race to the Top: Teen Numbers. In...

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Reflections on NCSM/NCTM, Part 2

Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are four staff members’ reflections on a session that stood out to them. (Read the first three here.) Keith: “The Iris Carl Equity Address: Equity and Agency from Inside the Classroom” by José Luis Vilson (NCTM) José Vilson began his talk with an elegant, powerful statement — “Equity is belonging.” — and then challenged us with this question: “Do you believe your students belong?”...

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Reflections on NCSM/NCTM, Part 1

Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are three staff members’ reflections on a session that stood out to them. Four more to follow next time. Keith: “From Oakland to Wakanda: Transforming Mathematics Classrooms to Become Empowering Spaces” by Imani Masters Goffney (NCTM) Imani Masters Goffney gave a fascinating talk about making math classrooms equitable spaces for learning. She used the movie Black Panther as a context...

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A Conversation about “Key Words”

In my years of leading in-person and online professional development, the idea of teaching students that certain “key words” signify a particular operation (e.g. “altogether means add”) often comes up when discussing story problems. People also generally see the power of the story problem routine that Investigations uses to support students in making sense of and solving story problems. This led me to start a conversation in a recent online course about the juxtaposition between the focus of...

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A Grade 5 Q&A: Percents

Question: Why was the work with percents taken out of the 5th grade curriculum in the 3rd edition? Answer: In the 1st and 2nd editions of Investigations, there was a unit (Name that Portion and What’s That Portion?) that included lessons that connected what 5th graders already knew about percents to what they already knew about fractions and decimals. These concepts were taught together, rather than separately, and built strong conceptual understandings of the meaning of percents and their...

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